Yes, it's very common to omit the verb when the question already includes that verb: - ¿Qué estás haciendo? (Estoy) Estudiando - ¿Cómo estás? (Estoy) Bien

ESTOY CANSADO Y TRABAJANDO- ESTOY TRABAJANDO Y CANSADO- ESTOY CANSADO Y TRABAJANDO A PESAR DE MI CANSANCIO- ¿ESTÁS DESCANSANDO O TRABAJANDO?...RESPUESTA,TRABAJANDO.

Yes, you can omit the verb "estoy", when the conversation is informal. Obviously, when it is an answer, but if it is a formal case it is necessary to write the complete sentence. "Estoy cansado, pero estoy trabajando."

to avoid redundancy in this sentence you can say: ESTOY CANSADO Y TRABAJANDO, ESTOY CANSADO Y TRABAJANDO IGUAL A PESAR DE MI CANSANCIO, trabajando without ESTOY sound good because it is understood that TRABAJANDO = ESTOY TRABAJANDO because the first and the second sentence are working together and both are one sentence (may be with same times or different times, differents word and so on, regardless of this both work toghether), both could too speak about the same idea, meaning, topic and so on (both could speak about the same but may be with same times or different times, different words and so on, regardless of this both work together)),) . if in a sentence TRABAJANDO is not understood that is ESTOY TRABAJANDO you must use ESTOY to keep CONCORDANCE AND MEANING. CONTEX CAN TOO MAKE IT IS UNDERTOOD.

Hola Bradenski, Tal vez una forma mas natural sería "a pesar de estar cansado, estoy trabajando" Un abrazo, Marina